Question

The base of a triangular pyramid is a triangle with corners at `(2 ,6 )`, `(4 ,3 )`, and `(3 ,8 )`. If the pyramid has a height of `6`, what is the pyramid's volume?

Answer 1

Volume pf pyramid `color(indico)(V_p =14)` cubic units

Explanation:

Volume of Triangular pyramid `V_p = (1/3) B H` where B is the base area of the triangle and H is the height of the pyramid.

`"the area (A) of the triangle can be found using the formula given the coordinates of the three vertices"`

`B=1/2[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]`

`color(red)(B =) [2(3-8) + (4(8-6) + 3(6-3)] = (-10 + 8 + 9) = color(red)(7)`

Volume pf pyramid `color(red)(V_p = (1/3) B H = (1/3) * 7 * 6 = color(red)(14)` cubic units